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Wednesday, November 12, 2014

Someone needs to explain the seasons to Willis Eschenbach and Stan Robertson at WUWT

Sou | 8:16 PM Go to the first of 23 comments. Add a comment

I started to write this article some time ago in response to an article by Wondering Willis Eschenbach (archived here). Today there's another article on the same topic by someone called Stan Robertson (archived here) so I figured I'd resurrect this. Stan's been featured here on a previous occasion.

The main question they are asking is: why doesn't Earth heat up more when it's closest to the sun, in January? The corollary they didn't ask is, why doesn't Earth cool down more when it's furthest from the sun, in July?

The main answer is: the tilt of the earth dominates seasonal variation, not distance from the Sun. For Earth that is. (It's different on Mars.) Plus - oceans.

This is a long and long-winded article, probably with too much repetition and a tad muddled. But I've spent enough time on it so click read on if you're up for it :)



Willis Eschenbach's Gaia-like hypothesis


Wondering Willis Eschenbach was touting his version of the Gaia hypothesis, that the Earth won't heat up (or presumably cool down) because it will regulate itself. He was arguing that small changes in incoming solar radiation over the eleven year solar cycle don't affect Earth's climate to any great extent.  In that he'd be correct. He also seemed to be also arguing that radiative forcing, no matter how big, won't affect Earth's climate either. In that he's incorrect. He wrote (my emphasis):
The climate system is not some inanimate object that is simply pushed around by external forcings. Instead, it reacts, it responds, it evolves and varies based on the instantaneous local situations everywhere. In particular, when it is cold we get less tropical clouds, and that increases the energy entering the system. And similarly, when it is warm we get more tropical clouds, cutting out huge amounts of incoming energy by reflecting it back to space. In this way, the system reacts to maintain the same temperature despite the changes in forcing.

That's Willis' version of the Gaia hypothesis or his thunderstorm hypothesis. It has an element of fact in that the hydrological cycle does moderate the surface temperature. However it's not nearly as simple as Willis makes out. That's not the only problem with what Willis wondered. He extends this notion to argue that Earth's "maintains the same temperature" even when there is a change in radiative forcing.

For starters, Willis is wrong if he thinks that Earth "maintains the same temperature". It doesn't, as is clearly demonstrated by the fact of glacial periods and interglacials, as well as by the recent rapid rise in surface temperatures. If Willis' hypothesis were all that happened, then the temperatures would be pretty well flat. But they haven't been.

Data source: NASA GISS


Why doesn't Earth heat and cool more as it orbits the Sun?


To get back to the main question, which is: why doesn't Earth's temperature fluctuate a whole lot more than it does as it gets closer to (and further from) the sun? At the beginning of his article, Willis puts up a chart that he says is "monthly variations in TSI (as a global 24/7 average) as shown by the CERES data".

Source: WUWT

Willis has plotted the flux at the top of atmosphere averaged over the globe. This has a seasonal component, reflecting the distance of Earth from the sun as it revolves in orbit. Willis asks a question, which was the main point of his article. Stan Robertson says it's a profound question:
My question is, if the tiny eleven-year changes in TSI of a quarter of a W/m2 cause an observable change in the temperature, then where is the effect of the ~ 22 W/m2 annual variation in the amount of sun hitting the earth? That annual change is a thousand times the size of the eleven-year TSI change. Where is the effect of that 22 W/m2 change?

I don't think it's a profound question but you may differ. I see quite a lot wrong with it. He's correct that there is a variation of about six or seven per cent in incoming solar radiation from maximum to minimum over the year. And yes, that is about 20 W/m2 difference from peak to trough. It's the difference between what's received in December/January (say 350 W/m2) and what's incoming in June/July (say 330W/m2), with the average over the year around 340W/m2.


Annual variation in global temperature


Stan Robertson has a question too. He asks:
First, why don’t we see some significant annual cyclic variation of global mean temperature? This is a truly profound question! It ought to keep climate modelers awake all night, every night. 

Well, we do see significant cyclic pattern to global surface temperature. I don't think too many climate modelers would be unaware of this. (Has Stan not heard of seasons?) I won't bother any more with Stan's article from here on in. He's written a lot of rubbish about clouds and cosmic rays and scientists staying awake all night, which you can read here if you want to.

Here is an estimate of the annual variation in the temperature on Earth, from NOAA:


Data source: NOAA
Over the year, the average for the twentieth century for the combined land and sea surface varied by 3.75°C from the coldest month to the warmest. Below you can see the difference between land and sea:

Data source: NOAA
Notice the sea temperature over the year - I'll come back to that a bit further down. The sea temperature doesn't change much over the year, it's the land that makes all the difference.

When it's winter in the Northern Hemisphere (December to February), the Arctic won't be getting much sunlight and large parts of the northern hemisphere that do would be reflecting a lot back to space, because of the snow cover. In addition, the nights are longer, so the land will be radiating out more than it gets in from the sun during the shorter day. In the southern hemisphere, there's a lot more ocean than land, and the surface temperature of the oceans doesn't fluctuate anything like the amount that land does.

In the Northern Hemisphere summer (June to August), the large land surface would get relatively hot (land heats up faster than the oceans). The southern hemisphere will have longer nights than days so will have more time to cool down. And again, the southern hemisphere is largely ocean, where the surface temperature doesn't change as much as it does on land.

So it's the Northern Hemisphere, with its much large land surfaces, that dominates the global surface temperature variation over the year.

From the TSI chart of Willis, the minimum TSI is in June and July and the maximum is in December and January. That's the opposite to the change in temperature over the year. Earth is furthest from the sun (aphelion) in the Northern Hemisphere summer, which is why incoming solar radiation is less at this time. It's about six per cent less in July (the Northern Hemisphere summer) than in January, when its at perihelion (closest to the sun).

Source: Sydney Observatory. Credit: Nick Lomb

It's the tilt that causes the seasons


But it's not the distance from the sun, and obviously not the reduced incoming short wave radiation, that causes Earth as a whole to be at its hottest from June to August. What dominates is the capacity of the larger land surface in the Northern Hemisphere to heat up when it's facing the sun.

The fact is that Earth is tilted on an angle of about 23.4° and points in the same direction while it orbits. This means that as Earth revolves around the sun over the year, different parts of Earth are facing the sun more than others. In the middle of the calendar year, the Northern Hemisphere is facing the sun and the southern hemisphere not so much. There are longer days in summer and longer nights in winter. Where the days are longer there is more energy coming in than going out, and where the days are shorter there is more energy being radiated out than coming in.

And no. I'm not about to give a lecture on how energy moves around the planet over days and night and seasons. If you are curious, there are some slides here that touches on the subject. Suffice to say that if greenhouse gases weren't accumulating, and there wasn't any other change in forcing, then over the year there'd be as much energy being radiated back to space as there was coming in from the sun.

There is also this article from NASA, which explains how it's the tilt of earth that dominates, not the distance from the sun:
In January, Earth makes its annual closest approach to the Sun -- an event astronomers call perihelion. Northerners shouldn't expect any relief from the cold, however. Although sunlight falling on Earth will be slightly more intense today than it is in July, winter will continue unabated.
"Seasonal weather patterns are shaped primarily by the 23.5-degree tilt of our planet's spin axis, not by Earth's elliptical orbit," explains George Lebo, a professor of astronomy at the University of Florida. "During northern winter the north pole is tilted away from the Sun. Days are short and that makes it cold. The fact that we're a little closer to the Sun in January doesn't make much difference. It's still chilly -- even here in Florida!"
The article also mentions how there is more intense sunlight in January than July, but the Southern Hemisphere oceans have a moderating influence when the earth is closest to the sun. It's summer here in January:
Earth's distance from the Sun doesn't change much throughout the year, but there are measurable differences in solar heating that result from our planet's slightly elliptical orbit.
"Averaged over the globe, sunlight falling on Earth in January [at perihelion] is about 7% more intense than it is in July [at aphelion]," says Roy Spencer of the Global Hydrology and Climate Center in Huntsville, AL. "The fact that the northern hemisphere of Earth has more land, while the southern hemisphere has more water, tends to moderate the impact of differences in sunlight between perihelion and aphelion."
Sunlight raises the temperature of continents more than it does oceans. (In other words, land has a lower heat capacity than water does.) In July (aphelion) the land-crowded northern half of our planet is tilted toward the Sun. Aphelion sunlight is a little weaker than sunlight at other times of the year, but it nevertheless does a good job warming the continents. In fact, say climate scientists, northern summer in July when the Sun is more distant than usual is a bit warmer than its southern counterpart in January.

This short video is from Wikipedia and shows Earth as seen daily from the Sun looking at UTC+02:00, showing the solstice and changing seasons.






What happens to incoming solar energy?


Which brings me to the next point. The amount of incoming shortwave radiation absorbed at the surface at different times of the year, compared to what is reflected. Then what happens after solar is absorbed at the surface. Here is the energy balance diagram from Wild12 as presented in the AR5 WG1 IPCC report. Click to enlarge it:


Figure 2.11: Global mean energy budget under present day climate conditions. Numbers state magnitudes of the individual energy fluxes in W/m2, adjusted within their uncertainty ranges to close the energy budgets. Numbers in parentheses attached to the energy fluxes cover the range of values in line with observational constraints. Figure adapted from Wild et al. (2013). Source: IPCC AR5 WG1 page 2-127

I've written about the global energy budget on previous occasions. The most detailed article is probably this one here.

Willis' ponders the seasonal variation in incoming solar radiation and writes:
To get an idea of the predicted effect of this variation in TSI, using IPCC figures this TSI change of 22 W/m2 is about the same change in forcing that we would get from six doublings of CO2 … that is to say, CO2 going from the current level (400 ppmv) to the extraordinary level of 25,600 ppmv.
The problem there is that his 22W/m2 isn't all plus. It builds up over six months from 330W/m2 in July to 350W/m2 in January and then drops back down over six months to 330W/min the following July. It's not as if it is plus 22W/m2 for half the year. The average over the year is 340W/m2.


Remember too that this difference that Willis talks about is at the top of the atmosphere. A lot of what hits the top of the atmosphere is reflected back out without ever getting to the surface of Earth. If the same proportion reached the surface all year around, then at the maximum in January, this would be only around 10 or 11W/m2 more than at the July minimum - not 22W/m2. Or a plus or minus around 5.5W/m2 around the annual average. In fact, the tilt of the earth has a much bigger impact on surface temperature than the plus and minus 5.5W/m2.


Temporary vs permanent forcing


Willis goes much further and claims:
In addition, again according to the IPCC, using their central value of 3°C warming per doubling of CO2 (3.7 W/m2 additional forcing), this change in forcing should be accompanied by a change in temperature of no less than 18°C (32°F).

What Willis is arguing here is that between July and January, the temperature should go up by 18°C and from January to July it should drop by 18°C. Which clearly doesn't happen. Apart from his numbers being wrong (see above), you can blame the absence of such huge temperature fluctuations on the atmosphere and oceans.  The earth isn't like the moon, it has the air and the oceans to moderate the weather and climate.

Earth is only getting the extra maximum amount of sunlight for a short period and of that, the part that gets through to the surface and isn't reflected, is falling on the southern hemisphere oceans, which have a large capacity for absorbing heat. In the Northern Hemisphere there is more heat leaving the surface because the nights are longer than the days. In the Southern Hemisphere, there is a much larger expanse of oceans relative to land. Oceans don't heat up as fast as the land does. Willis continues:
Now, I can accept that this would be somewhat reduced because of the thermal lag of the climate system. But the transient (immediate) climate response to increased forcing is said to be on the order of 2°C per doubling of CO2. So this still should result in a warming of 12°C (22°F) … and we see nothing of the sort.

Again, Willis seems to be assuming that all the sunlight at the top of atmosphere reaches the surface, which it doesn't. Check the energy diagram above. Almost one third is reflected straight back out. Some is absorbed in the atmosphere and less than half incoming solar energy actually gets to the surface. I worked out above that the difference in January and July would be around plus and minus 5W/m2 at the surface compared to the average. So if all else were equal (which it isn't), you'd be looking at January being around 2.7 degrees cooler and July being about 2.7 degrees warmer if the solar energy came in at a constant rate all year around. I've assumed 2 degrees per additional 3.7W/m2. (That's less than the difference between the January and July global average combined temperature, and around a quarter the difference between the January and July global land only temperature.)

However as I said, all else is not equal.

Willis is also assuming that the fluctuation in incoming solar radiation will all result in a temperature rise in the surface itself. Look again at the energy diagram and think about where the extra sunlight is being directed. At the time of the year when there is most incoming solar radiation, it's summer down south where most will fall on the oceans, which has a large capacity for storing heat. Some will heat up the oceans, some will go into evaporating water with no immediate temperature change. Meanwhile, the long nights up north would be radiating out more than is coming in during the day.

On the other hand, when less TSI is coming in, it's the Northern Hemisphere summer. So there's less incoming solar being absorbed on all that land during those long summer days. At the same time, the oceans (and land) in the Southern Hemisphere are radiating out more than is coming in, because the nights are longer.

If the earth was closest to the sun in the Northern Hemisphere summer, then I'd think the effect would be more evident.


Wet and dry seasons in the tropics are not all the same


Willis continues and muses about tropical clouds:
I say this lack of an effect of the TSI changes is because the climate system responds to the current conditions. The climate system is not some inanimate object that is simply pushed around by external forcings. Instead, it reacts, it responds, it evolves and varies based on the instantaneous local situations everywhere. In particular, when it is cold we get less tropical clouds, and that increases the energy entering the system. And similarly, when it is warm we get more tropical clouds, cutting out huge amounts of incoming energy by reflecting it back to space. In this way, the system reacts to maintain the same temperature despite the changes in forcing.

Here Willis seems to be mixing up weather in the tropics with winter in the Northern Hemisphere. What he doesn't explain is that since he's claiming that tropical clouds are the reason for not getting hotter in the perihelion, which tropical clouds would they be? The Southern Hemisphere wet season? What about the Northern Hemisphere wet season? What does that do to his theory?

In the Southern Hemisphere, such as Australia, the tropical wet season is roughly October to March.  In the Northern Hemisphere, like in India, the wet season is roughly April to September. There's generally a wet season somewhere in the tropics - at any time of year. So although Willis is correct in that the hydrological cycle is important in energy distribution, that doesn't explain why there isn't his temperature difference of 18°C or 12°C over the year (which estimate is way too high anyway).


Changes in temperature are driven by changes in forcing


Willis restates his question:
However, I’m happy to listen to alternate explanations and to consider opposing evidence … so if you think that the IPCC is right when it says that changes in temperature are driven by the changes in forcing, I ask you why the annual forcing change of 22 W/m2 doesn’t seem to show a corresponding 12°C change in global temperature.

Now the IPCC is right when it says that changes in temperature are driven by changes in forcing. It's pretty well a truism. The IPCC definition of radiative forcing is:
‘the change in net (down minus up) irradiance (solar plus longwave; in W m–2) at the tropopause after allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values'.

Which is why Willis' question is wrongly posed. The change in net (down minus up) irradiance (solar plus longwave) averaged over the year is not 22 W/m2. It's more like 0.6 W/m2.  And that's got nothing to do with Earth's orbit. It's all to do with the accumulating greenhouse gases.

Finally and to reiterate the point, although there is a seasonal cycle to surface temperatures, it is because of the angle of tilt of Earth, which governs the seasons. Over the year, the distance from the sun has much less effect on surface temperature and weather, than the orientation to the sun. Proximity to the sun ends up having not a great effect on surface temperature over the year.

Below is a short video from NASA about how satellites are used to help track changes over time. Click in the bottom left to view it on youtube or full screen.





From the WUWT comments

Not too many. The article was too long as it is.

Doug Proctor wonders if the climate is squishy or rigid (extract):
November 11, 2014 at 9:43 pm
...The skeptic position as I see it, and the one I hold, is that the current 22 W/m2 variation has been evened out to prduce the world we have today, but that it is not a fixed state dependend on the exact 22 W/m2 arriving when and where it does, but a more-or-less fixed state requiring a significant change to modify it at all, and not in a chaotic way. If a doublly of CO2 is 3.5 W/m2, then the energy redistribution system would be 22 working up and down from a general 341.5 + 3.5 W/m2. We’d hardly notice it.
It all comes down to our climate being squishy or rigid in the face of solar heating.

David Riser is quite confused about TSI:
October 25, 2014 at 7:27 pm
So, if I read this right, your point is that the earths orbit creates a 22W/M-squared change based on our distance from the sun. Which is vastly greater than the variation of TSI or any component of it. If this is true then your cloud based negative feedback system is most likely correct, or we would have frozen or fried a long time ago.
Would you suppose that the issue then is not too much energy (earth seems to handle that fine) but what about if the incoming energy is insufficient to maintain current temps, could that be a driver to the occasional abrupt cold shift. Since I am reasonably sure that no one disregards the Ice Ages.
Anyhow, I have to agree Willis, you continue to make a sound argument. 

Roger doesn't seem to know that Earth has had glacial and interglacial periods in the past:
October 25, 2014 at 7:33 pm
Systems that are stable (and our climate has been stable for millions of years) contain negative feedback. How else could they remain stable. Is it credible that we could have lasted this long without a mechanism (like clouds reflecting light) providing negative feeddack? If a “tipping point” existed, wouldn’t something have pushed us past it already? 

23 comments:

GSR said...

This stuff is easy for you to write SOU given that you have institutional sponsorship for every acronym you type.

It's time to fess-up SOU. Is it OSU, ANU, UAH that's been bankrolling your blogging?

It's plain for all to see that you have been bought by institutions possessing 2 vowels and a consonant. (Which means that for the first time since 2009, UEA is off the off the hook )

GSR said...

BTW great piece Sou

Robert Murphy said...

Wondering Willis, once again demonstrating that the people who claim that climate is unchanging are in fact the "skeptics", not the scientists. It's apparently kept constant by invisible pink unicorns and magic pixie dust. What happened to "Of course climate is changing, it changes all the time, and did so long before SUV's!! (and Al Gore is fat!)"? "Skeptics": consistently inconsistent.

George Montgomery said...

Willis's and Stan's articles are all a bit déjà vu, with elements of Richard Lindzen's Iris Hypothesis (2001), etc. Both articles may be an illustration of a skeptic philosophy that the earth's climate is naturally self-regulating in the long run and any changes are gradual. It may be a continuation of the 'original' skeptics argument over the decades against Svante Arrhenius' theory i.e. the skeptic belief that more clouds would stabilise earth's temperatures as encapsulated in Rossby (1959). And Rossby or one of his books could be the catalyst for Bob T's pre-occupation with ENSO. I'll stop now with the conjecture. Speaking of Svante Arrhenius, at least 97 per cent of WUWT commenters can't pronounce his name correctly and you can bet London-to-a-brick on that.

Anonymous said...

I thought TSI was about 1360 W/m^2. Why do the graphs and text talk about TSI being about 340 W/m^2. What am I missing?

William Connolley said...

RT has a post up: http://quantpalaeo.wordpress.com/2014/11/12/q-why-are-there-no-intra-annual-patterns-in-global-temperature-anomalies/ which may well provide an even more fundamental reason why WE isn't seeing the variations he expects.

I *think* he's right. If he is, the good news is that WE and WUWT is even more crap that we thought. But the bad news is that you (and I, though at least I didn't write a post about it) didn't spot it.

Sou said...

You know, GSR, last time you wrote something like that (well, not exactly, but you know what I mean), it ended up being woven into a conspiracy theory about me by a credulous commenter at WUWT. Maybe this time someone will decide that the no-name anonymous OAS is bankrolling HW :)

Sou said...

William, thanks for that. That's where Stan Robertson went wrong in today's article. A number of people at WUWT pointed this out to Stan, in the comments.

I don't know about Willis. I think Willis knows this about anomalies. I don't think he made that mistake in his article.

Sou said...

If Earth were a flat plane then it's 1360 W/m^2 or thereabouts.

Since it's not a flat plane, the 340W/m^2 is what Earth gets averaged over the whole surface. Remembering that half the Earth is dark at any time, and its shape is more like a sphere.

http://en.wikipedia.org/wiki/Solar_constant#Solar_irradiance

Also, see 4.1 of Wild et al 2012:
http://www.iac.ethz.ch/doc/publications/Wild_etal_GlobalEnergyBalance_ClimDyn2012.pdf

...and Then There's Physics said...

I didn't read all of Willis's article (as WMC would say "why would I?") but my immediate thought was the same as Richard Telford's "they're anomalies, so why would you expect to see an annual variation?"

t_p_hamilton said...

Divide by 4 to account for the surface area of a sphere divided by the area of a circle.

...and Then There's Physics said...

I'll also have a go. The point is that only one side of the Earth faces the Sun and the area over which it intercepts solar radiation is the cross-sectional area (pi R^2) not the actual surface area (4 pi R^2). If the solar flux is 1360W/m^2, then the amount of energy the Earth intercepts every second is 1360 x pi R^2. To then get the amount of energy received per square metre of the actual Earth's surface, you need to divide that by 4 pi R^2 (as mentioned above) to get 340 W/m^2 (i.e., 1360/4).

Anonymous said...

So the number "340"" is the "disk averaged TSI" not the TSI as defined canonically for a flat surface ("1360"). The name is the same (TSI), the units are the same (W/m^2) but the definition (physical configuration of system) is different. Interesting confusion. Analogous to the difference between "h" and "h-bar" in "modern physics."

Anonymous said...

More like the "sphere averaged TSI".

Henk said...

There is still one important point you don't mention. The earth recieves exactly the same amount of solar energy between 21st of march and the 23rd of september as it does between sep 23 and march 21, because when it is further away it moves slower and when it is close to the sun it moves faster in its orbit around the sun, according to Kepler's 2nd law.

numerobis said...

How does that work? Earth isn't going to be dodging rays by moving faster.

palindrom said...

Nothing so fancy as that -- it's simply that there's more time between the March and September equinoxes, because the earth isn't moving as fast. I'm not sure about 'exactly", though, since the insolation effect goes as the square of the distance and the transverse orbit speed as the inverse first power of the distance, so off the top of my head I don't think they'll cancel.

adelady said...

Lawks!

I've always kept a classroom globe and a torch handy when tutoring English. It's one thing for kids to learn the words for the names of the seasons and the logic of linking certain activities or weather events to them. When they ask the eternal Whyyy? question, you have to be ready to explain how things work on a tilted globe. And explain again, and again, and again - especially when some bright spark brings up the question of day and night and time differences.

As it happens, these things can be explained in simple, non-scientific language - to 10 year olds. All it takes is a bit of time and guided explanations for one or more kids handling the physical object for themselves. (Or a team effort nominating others as the sun - prime job, you get to hold the torch - or as a resident of another point on the globe.)

I've never tried to do anything scientific/climate related with an older student, but I'm pretty sure most could get the idea in a couple of sessions.

cRR Kampen said...

Are you trying to say that the time span of near-exactly a half year is like a year between the 21st of March and the 23rd of September whereas the other half year is about three months between the 23rd of September and the 21st of March?

"it's simply that there's more time between the March and September equinoxes, because the earth isn't moving as fast." - I think you really need to rephrase this. Six months is six months.

palindrom said...

cRR Kampen:

"Six months is six months .... "

No, not quite. As an example, the table at

http://aa.usno.navy.mil/data/docs/EarthSeasons.php

shows that successive equinoxes occurred at

2013 Sep 22 at 20 44 UT = JD 2456558.364
2014 Mar 20 at 16 57 UT = JD 2456737.206
2014 Sep 23 at 02 29 UT = JD 2456923.603

The last column is the Julian date, which is a sequential day number that is used to compute time intervals over long spans. I computed the JDs myself, using software I've used for many years. Subtracting these reveals that the time between the September and March equinoxes is 178.84 days, while the time between the March and September equinoxes is 189.40 days. The reason is the one cited by Henk -- when the earth is farther from the sun, it moves slower in its orbit, by Kepler's second law, which is exactly equivalent to conservation of angular momentum.

palindrom said...

I should add that of course it's still the case that the instantaneous flux per unit area at earth is lower in (say) July than in January; the extra length of the Northern summer only matters to the extent that heat builds up over time. The north does have more time to accumulate heat in the summer than the south does.

palindrom said...

Oops, I think that Henk is actually correct that the cancellation is exact, contrary to the off-the-cuff assessment in my in my 3:00 PM response. I was thinking there of the linear speed of the earth, which does fall as 1/r; however, the relevant quantity is actually the angular speed of the earth in its orbit ("omega" in physics notation), which is v/r.
The extra power of 1/r makes the angular speed proportional to 1/r-squared. Consequently, the time it takes the earth to move (say) one degree in its orbit is proportional to r-squared, exactly compensating the inverse-square radiation law.

Equal angular displacements of the earth in its orbit (e.g. the 180-degree displacement going from one equinox to the next) therefore do correspond to equal amounts of radiant energy intercepted.

numerobis said...

Oh neat, I hadn't considered that the equinoxes weren't at precisely 6 months from each other.

So the conclusion: insolation/angle is constant. The summer season can reasonably be defined by an angle (say 90 degrees), by which definition the southern summer and northern summer get precisely the same amount of insolation -- us Northerners just get more days of summer.

I guess the orbital dynamics also imply that the days get shorter faster in Northern autumn. Which further implies I should move to the southern hemisphere, because my SAD is activated by the derivative rather than by mere lack of sun (I'm happier two weeks after the winter solstice, as the days lengthen, than a month before it).